Consider a hollow metal cylinder of radius 1.0 mm that has a thin wire of radius 0.50 mm running down the center as sketched in Figure P18.46. This structure is a capacitor, with the wire acting as one “plate” and the cylinder acting as the other plate. Calculate the capacitance using the following steps. (a) Place charges Q on the wire and the cylinder and calculate the electric field between them. Assume the cylinder has a length L and assume L is very long. (b) Estimate qualitatively the electric potential difference between the wire and the cylinder, which can be done using a plot of the electric field as a function of radius. (c) Use the potential difference to find the capacitance C for L=_ 10 cm.
Figure P18.46
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